90
Chapter 7 Some Dimers of Triatomic Radicals with 17 and 19 Valence-Shell Electrons
of the electronic structure of NO 2 is assumed to occur when NO 2 dimerizes, then it
has been argued that spin-pairing of the nitrogen odd-electron charge of 0.5 for
each monomer generates an N-N σ-bond-number of 0.5 for the dimer, i.e. one half
of an N-N electron-pair is formed for the N 2 O 4 dimer. This argument is not valid
7b,
10
. Inspection of the valence-bond structures (3)-(5) shows that a nitrogen atom
can share its odd-electron charge to form a “long” N-O bond as well as the N-N
bond. Consequently, if the nitrogen odd-electron charge for NO 2 is 0.5
i
, resonance
between the N 2 O 4 Lewis structures (3)-(6) generates an N-N bond-number of 0.25.
Each of the 16 N 2 O 4 Lewis structures (such as (3)-(7)) obeys the LewisLangmuir octet rule for atoms of first-row elements (Section 2-4a), and twelve of
these structures have a “long-bond” linking a pair of non-adjacent atoms. Why
should these latter structures be considered to be of importance for the groundstate resonance description of N 2 O 4 ? In Section 2-4, we have referred to the
electroneutrality principle, which states that if atoms of a neutral molecule have
similar electronegativities, the atomic formal charges for the ground-state of the
molecule will have small magnitudes. For N 2 O 4 , appreciable weights for at least
some of the “long-bond” structures such as (4)-(7) (whose formal charges are
smaller than are those for the standard Lewis structure (3)) help ensure that this
requirement is satisfied.
Because each NO 2 moiety of structures (3)-(7) has 17 valence-shell electrons,
these structures will be designated as “covalent” structures with the electron
distributions of NO 2 NO 2 . In Section 7-3, “ionic” or charge-transfer structures of
the type
2
2
NO NO
(or
2
2
NO NO
) will also be included in the description of the
electronic structure. As is the case for H 2 (Section 3-3), the ionic structures are
less important than are the corresponding covalent structures for the ground-state
resonance
7b, c, 10
.
Molecular orbital calculations for NO 2 and N 2 O 4 , with configuration interaction
(C.I.) (Sections 3-3 and 10-3) included for N 2 O 4 , have been parameterized so that
the experimental values for the first two ionization potentials of NO 2 , the first
ionization potential of N 2 O 4 , and the nitrogen odd-electron charge of NO 2 (Section
6-1) are reproduced
7b, c, 13 . The NO 2 parameters have been transferred into the
N 2 O 4 calculations. From the resulting molecular orbital-CI wave-function for
N 2 O 4 , weights of 0.24, 0.24, 0.24, 0.13 and 0.13 have been calculated for sets of
covalent structures of types (3)-(7). The remaining weight of 0.02 is shared
amongst various ionic structures. The covalent weights are similar to those obtained from spin-pairing the odd-electrons of two NO 2 monomers with nitrogen oddelectron charges of 0.5, namely 0.25, 0.25, 0.25, 0.125 and 0.125, and support the
hypothesis that dimerization of NO 2 involves primarily the spin-pairing of the
odd-electrons of two NO 2 radicals.
The odd-electron of NO 2 is delocalized amongst a nitrogen hybrid atomic
orbital and the oxygen 2p -orbitals that overlap with this nitrogen orbital. The
three orbitals are displayed in Figure 6-1. The atomic orbitals whose occupancies
i To obtain a nitrogen odd- electron charge of 0.5, the NO2 structures (1) and (2) must have
equal weights. Therefore, the weights for the N2O4 structures (3)-(6) are each equal to 0.25.
Chapter 7 Some Dimers of Triatomic Radicals with 17 and 19 Valence-Shell Electrons
of the electronic structure of NO 2 is assumed to occur when NO 2 dimerizes, then it
has been argued that spin-pairing of the nitrogen odd-electron charge of 0.5 for
each monomer generates an N-N σ-bond-number of 0.5 for the dimer, i.e. one half
of an N-N electron-pair is formed for the N 2 O 4 dimer. This argument is not valid
7b,
10
. Inspection of the valence-bond structures (3)-(5) shows that a nitrogen atom
can share its odd-electron charge to form a “long” N-O bond as well as the N-N
bond. Consequently, if the nitrogen odd-electron charge for NO 2 is 0.5
i
, resonance
between the N 2 O 4 Lewis structures (3)-(6) generates an N-N bond-number of 0.25.
Each of the 16 N 2 O 4 Lewis structures (such as (3)-(7)) obeys the LewisLangmuir octet rule for atoms of first-row elements (Section 2-4a), and twelve of
these structures have a “long-bond” linking a pair of non-adjacent atoms. Why
should these latter structures be considered to be of importance for the groundstate resonance description of N 2 O 4 ? In Section 2-4, we have referred to the
electroneutrality principle, which states that if atoms of a neutral molecule have
similar electronegativities, the atomic formal charges for the ground-state of the
molecule will have small magnitudes. For N 2 O 4 , appreciable weights for at least
some of the “long-bond” structures such as (4)-(7) (whose formal charges are
smaller than are those for the standard Lewis structure (3)) help ensure that this
requirement is satisfied.
Because each NO 2 moiety of structures (3)-(7) has 17 valence-shell electrons,
these structures will be designated as “covalent” structures with the electron
distributions of NO 2 NO 2 . In Section 7-3, “ionic” or charge-transfer structures of
the type
2
2
NO NO
(or
2
2
NO NO
) will also be included in the description of the
electronic structure. As is the case for H 2 (Section 3-3), the ionic structures are
less important than are the corresponding covalent structures for the ground-state
resonance
7b, c, 10
.
Molecular orbital calculations for NO 2 and N 2 O 4 , with configuration interaction
(C.I.) (Sections 3-3 and 10-3) included for N 2 O 4 , have been parameterized so that
the experimental values for the first two ionization potentials of NO 2 , the first
ionization potential of N 2 O 4 , and the nitrogen odd-electron charge of NO 2 (Section
6-1) are reproduced
7b, c, 13 . The NO 2 parameters have been transferred into the
N 2 O 4 calculations. From the resulting molecular orbital-CI wave-function for
N 2 O 4 , weights of 0.24, 0.24, 0.24, 0.13 and 0.13 have been calculated for sets of
covalent structures of types (3)-(7). The remaining weight of 0.02 is shared
amongst various ionic structures. The covalent weights are similar to those obtained from spin-pairing the odd-electrons of two NO 2 monomers with nitrogen oddelectron charges of 0.5, namely 0.25, 0.25, 0.25, 0.125 and 0.125, and support the
hypothesis that dimerization of NO 2 involves primarily the spin-pairing of the
odd-electrons of two NO 2 radicals.
The odd-electron of NO 2 is delocalized amongst a nitrogen hybrid atomic
orbital and the oxygen 2p -orbitals that overlap with this nitrogen orbital. The
three orbitals are displayed in Figure 6-1. The atomic orbitals whose occupancies
i To obtain a nitrogen odd- electron charge of 0.5, the NO2 structures (1) and (2) must have
equal weights. Therefore, the weights for the N2O4 structures (3)-(6) are each equal to 0.25.